K323 is the locus of P whose cevian triangle is perspective (at Q) to the 2nd Sharygin triangle. The locus of Q is K961 = pK(X1914, X8301). Compare with K132. See also K673.

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K323 is the cornerstone of a group of 12 cubics all related between themselves under isogonal, isotomic, G-Hirst conjugations – denoted g, t, h in the following diagram – or a product of these such as e = gtg which is X(32)-isoconjugation. All these cubics are weak cubics and contain a good number of ETC centers.

A similar group of strong cubics is obtained when K323 is replaced with K718. See also Table 68.